8tan(x)^2-3=7tan(2x)+21?

Answer 1

Are you sure you wrote that correctly?

The general plan of attack on these is to use trig identities to transform the equation into a rational or polynomial equation in a trig function of x. But while I'm seeing various ways to get a quartic equation in sin x, cos x, or tan x, I'm not seeing any ways to, for example, get a quadratic equation in cos^2 or tan^2.